On analytic contravariant functors on free groups

Abstract : Working over a field $k$ of characteristic zero, the category of analytic contravariant functors on the category of finitely-generated free groups is shown to be equivalent to the category of representations of the $k$-linear category associated to the Lie operad. The proof uses the original Ginzburg-Kapranov approach to Koszul duality of binary quadratic operads. The equivalence is made explicit using the $k$-linear category associated to the operad encoding unital associative algebras, which provides the appropriate `twisting bimodule'.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-03367098
Contributor : Geoffrey Powell Connect in order to contact the contributor
Submitted on : Wednesday, October 6, 2021 - 9:25:49 AM
Last modification on : Saturday, January 29, 2022 - 3:34:43 AM

Identifiers

• HAL Id : hal-03367098, version 1
• ARXIV : 2110.01934

Citation

Geoffrey Powell. On analytic contravariant functors on free groups. 2021. ⟨hal-03367098⟩

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